The mean-Value at Risk static portfolio optimization using genetic algorithm

Abstract

In this paper we solve the problem of static portfolio allocation based on historical Value at Risk (VaR) by using genetic algorithm (GA). VaR is a predominantly used measure of risk of extreme quantiles in modern finance. For estimation of historical static portfolio VaR, calculation of time series of portfolio returns is required. To avoid daily recalculations of proportion of capital invested in portfolio assets, we introduce a novel set of weight parameters based on proportion of shares. Optimal portfolio allocation in the VaR context is computationally very complex since VaR is not a coherent risk metric while number of local optima increases exponentially with the number of securities. We presented two different single-objective and a multiobjective technique for generating mean-VaR efficient frontiers. Results document good risk/reward characteristics of solution portfolios while there is a trade-off between the ability to control diversity of solutions and computation time.